 | Alexander Malcolm - 1718 - 396 σελίδες
...Remainder is the other middle Term. Profofition 3d, IN an Arithmetical Progrejjion, (V. Definition 5th) the Sum of the Extremes is equal to the Sum of any two Terms, at equal Diilance from them ; or to double the middle Term (if the Number of Terms are odd;... | |
 | Samuel Webber - 1808 - 466 σελίδες
...being as their circumferences, the circumferences are also in arithmetical progression. But in such a, progression the sum of the extremes is equal to the sum of each two terms, equally distant from them ; therefore the sum of the circumferences on AC and CB is... | |
 | Ferdinand Rudolph Hassler - 1826 - 224 σελίδες
...proportion that the sum of the extremes is equal to the sum of the means, so it is evident that here the sum of the extremes is equal to the sum of any two terms equally distant from them, for the sum of every such pair of terms must contain the first... | |
 | Jeremiah Day - 1827 - 352 σελίδες
...the same in«er. a+4d, a+3«/, a + 2d, a-\-d, a. The sums will be 2a + 4d,2a+4<Z,2a+4d,2a+4d,2a44rf Here we discover the important property, that, 428. In an arithmetical progression, THE SUM or THE EXTREMES IS EQUAL TO THE SUM OF ANY OTHER TWO TERMS EQUALLY DISTANT FROM THE EXTREMES. In the... | |
 | Alexander Ingram - 1830 - 458 σελίδες
...the nth term is n — 1. Cor. — Hence y = a + (n — l)d, and a =y — (n — l)d. PROP. II. — The sum of the extremes is equal to the sum of any two terms equally distant from them. For any term exceeds the least, as much as its corresponding term... | |
 | Samuel YOUNG (of Manchester.) - 1833 - 272 σελίδες
...of terms, and the sum of the series ; having any three given, the other two may be found. Theorem. The sum of the extremes is equal to the sum of any two means equally distant from them. PROBLEM I. Given the extremes and number of terms to find the... | |
 | 1834 - 182 σελίδες
...quantities form an ascending geometric series, the sum of the first and last terms is always greater than the sum of any other two terms equally distant from the extremes. 68. Prove that if any quantities, whose differences are inconsiderable with respect to the quantities... | |
 | 1836 - 488 σελίδες
...the greatest. In a descending series, the first term is the greatest, and the last term the least. In arithmetical progression, the sum of the extremes,...other two terms equally distant from the extremes. The sum of the terms is equal to half the sum of the extremes multiplied into the number of terms.... | |
 | Silas Totten - 1836 - 320 σελίδες
...give certain properties of arithmetical progressions, without demonstrations.* (61.) 1st. In every arithmetical progression, the sum of the extremes is equal to the sum of any two terms equally distant from them ; or, equal to double the middle term, when there is an odd number... | |
 | George Willson - 1836 - 202 σελίδες
...difference. The numbers themselves are called terms, and the first and last terms extremes. PROPOSITION I. The sum of the extremes is equal to the sum of any two terms equidistant from them. Thus, in the series 2, 4, 6, 8, 10; 2+10=12, and 4 + 8=12. The reason... | |
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Here we discover the important property, that, in an arithmetical progression, the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes. 
